What’s it: Nash equilibrium is a game theory concept that determines the optimal solution in non-cooperative competition in which each player has no incentive to change their initial strategy. John Nash, an American mathematician, put it in 1950.
Nash’s solution is essential for explaining the oligopoly market. The assumption is that each player knows the equilibrium strategy of the other players. The Nash equilibrium is reached when no firm can increase profits by changing prices unilaterally. Each company tries to maximize its own profit considering the responses of its competitors.
Each company anticipates how its competitors will respond. They construct various scenarios regarding the possible responses of other players and use them to make profit-maximizing decisions. Therefore, firms in the market have strategic dependence but are not cooperative. I mean, they don’t cooperate and collude to maximize mutual benefits.
Nash Equilibrium Example
Nash equilibrium is a key game theory concept that conceptualizes players’ behavior and interactions to determine the best outcome. It is possible to predict the decisions of the players if they make decisions at the same time. And, decision making by each player will take into account the decisions of other players.
Say, there are two competing companies, namely Company ABC and Company XYZ. The two companies want to determine whether they should differentiate their product or not (homogeneous).
If the two companies differentiate products, each company will attract 100 new customers. If only one company decides to differentiate, it will attract 200 new customers, while the other companies will not attract new customers. If the two companies decide not to differentiate, neither company will attract new customers.
Company ABC had to differentiate its products because this strategy gives better results. Likewise, company XYZ considers the strategy and possible outcomes of company ABC. Company XYZ will also choose differentiation because it can add new customers. So, the scenario in which the two companies differentiate their products is a Nash equilibrium.
Say, for such differentiation strategies, both can charge either a high price or a low price. The market results under 4 different scenarios (measured by net income) are illustrated in the figure below.
The maximum combined profit occurs when the two companies charge a high price (lower right corner), $1,000. Company ABC earns a net profit of $600, and company XYZ receives $400.
However, in this case, Company XYZ has another option. The company can increase its net income from $400 to $450 if it charges a low price, and company ABC charges a high price.
Company ABC can only maximize its net income if the company XYZ agrees to charge a high price.
However, the company XYZ likely won’t. The company has the opportunity to get a higher net profit (i.e., from $400-450).
To solve such a situation, the company ABC will try to persuade the company XYZ to charge a high price by providing incentives. The incentive amount must be higher than the net profit lost when the company XYZ sets a high price, $50 ($450-$400).
Implications and why important
In a Nash equilibrium, each player will make the best decision for itself, based on the scenario of the decision the other party is likely to make. Each will create the best and most likely scenario. So, no one can do better by changing strategy.
In the real world, economists use the Nash equilibrium to predict how firms will respond to their competitors’ prices.
If the market consists of two players, collusion is likely the best and profitable outcome for both. At first, the two did not cooperate. After building some best-case scenarios about competitive output, the two may realize that collusion is the best solution in developing a pricing strategy.
Take the last previous example. After creating the scenario, company ABC and company XYZ realized that the market profit would be maximized if both charged high prices. Company ABC is likely to provide incentives to company XYZ.
Likewise, company XYZ is likely to negotiate such incentives. Otherwise, the company will take a low price as a solution to maximize its own profit.
Let’s say company ABC shares the profits with company XYZ of $60. The company ABC still allows them to receive a $540 profit, which is higher than $400 if company XYZ charges a low price.
On the other hand, for company XYZ, an additional $60 increases profits to $ 460 when charging a high price. This is higher than the maximum profit when the company charges a low price ($450).
Such behavior is known as collusion and is illegal in most countries. When collusive agreements are made openly and formally, companies form a cartel.
Collusion generates high prices in the market and hurts consumers. Because it violates the principles of fair competition, the government will closely monitor the market. And, in general, the scrutiny will be tighter if the market is composed of fewer players because the likelihood of collusive behavior is higher.